1) To make the dough: Combine all of the dough ingredients and mix and knead them, by hand, mixer, or bread machine, until you have a soft, smooth dough.
2) Allow the dough to rise, covered, for about 2 hours, or until it's puffy and nearly doubled in bulk.
3) Gently deflate the dough, and transfer it to a lightly greased work surface.
4) Pat and roll the dough into a rectangle about 18" x 14".
5) Make the cinnamon filling: Mix the Baker's Cinnamon Filling and water to make a smooth paste.
6) Looking at the dough horizontally (so it's 18" long), spread half the filling down the center third of the dough
7) Slice each banana into about 12 rounds. Space the slices atop the filling.
8) Fold one of the end pieces into the center to cover the bananas and filling.
9) Spread the remaining filling atop the piece of dough you've just folded into the center, and distribute the dried pineapple evenly atop the filling.
10) Fold the other side of the dough over the filling to cover it. Pull the long side seam underneath, and tuck each end underneath, too. You should have a long, flat log with no filling showing.
11) Use a sharp knife to cut 4 diagonal slashes atop the loaf, cutting through both layers of dough; this will allow steam to escape.
12) Brush with the beaten egg white, and sprinkle with the coarse or Demerara sugar.
13) Cover the loaf gently with lightly greased plastic wrap, and allow it to rest for 1 hour. It won't rise much, if at all. Towards the end of the resting period, preheat the oven to 375°F.
14) Bake the loaf in the middle of the oven for 25 minutes. Tent with foil, and bake for an additional 20 to 25 minutes, till it's golden brown and a sharp knife poked into the center doesn't reveal any raw dough.
15) Remove from the oven, and transfer to a rack to cool.
Yield: 1 large loaf, about 16 servings.